Opties van auto.arima() verkennen

De functie auto.arima() moet veel verschillende modellen schatten, en er worden verschillende snelkoppelingen gebruikt om de functie zo snel mogelijk te maken. Daardoor kan een model worden teruggegeven dat niet de kleinste AICc-waarde heeft. Laat auto.arima() harder werken om een goed model te vinden door het optionele argument stepwise = FALSE toe te voegen, zodat er naar een veel grotere verzameling modellen wordt gekeken.

Hier ga je proberen een ARIMA-model te vinden voor de vooraf geladen a10-gegevens, die maandelijkse subsidies voor anti-diabetica in Australië bevatten van 1991 tot 2008, in miljoenen Australische dollars. Bekijk ze eerst in de console voordat je aan deze oefening begint.

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Oefeninstructies

Gebruik de standaardopties in auto.arima() om een ARIMA-model voor a10 te vinden en sla dit op als fit1.
Gebruik auto.arima() zonder stapsgewijze zoekprocedure om een ARIMA-model voor a10 te vinden en sla dit op als fit2.
Voer summary() uit voor zowel fit1 als fit2 in je console, en gebruik dit om het betere model te bepalen. Wat is de AICc-waarde, op 2 decimalen afgerond? Ken het getal toe aan AICc.
Plot ten slotte, met het beste model op basis van AICc, de voorspellingen voor 2 jaar vooruit. Stel h hierop in.

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Find an ARIMA model for a10
fit1 <- ___

# Don't use a stepwise search
fit2 <- ___

# AICc of better model
AICc <- ___

# Compute 2-year forecasts from better model
___ %>% ___ %>% ___

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The first thing to do in any data analysis task is to plot the data. Graphs enable many features of the data to be visualized, including patterns, unusual observations, and changes over time. The features that are seen in plots of the data must then be incorporated, as far as possible, into the forecasting methods to be used.

Exercise 1: Welcome to Forecasting Using R Exercise 2: Creating time series objects in R Exercise 3: Time series plots Exercise 4: Seasonal plots Exercise 5: Trends, seasonality, and cyclicity Exercise 6: Autocorrelation of non-seasonal time series Exercise 7: Autocorrelation of seasonal and cyclic time series Exercise 8: Match the ACF to the time series Exercise 9: White noise Exercise 10: Stock prices and white noise

In this chapter, you will learn general tools that are useful for many different forecasting situations. It will describe some methods for benchmark forecasting, methods for checking whether a forecasting method has adequately utilized the available information, and methods for measuring forecast accuracy. Each of the tools discussed in this chapter will be used repeatedly in subsequent chapters as you develop and explore a range of forecasting methods.

Exercise 1: Forecasts and potential futures Exercise 2: Naive forecasting methods Exercise 3: Fitted values and residuals Exercise 4: Checking time series residuals Exercise 5: Training and test sets Exercise 6: Evaluating forecast accuracy of non-seasonal methods Exercise 7: Evaluating forecast accuracy of seasonal methods Exercise 8: Do I have a good forecasting model?Exercise 9: Time series cross-validation Exercise 10: Using tsCV() for time series cross-validation

Forecasts produced using exponential smoothing methods are weighted averages of past observations, with the weights decaying exponentially as the observations get older. In other words, the more recent the observation, the higher the associated weight. This framework generates reliable forecasts quickly and for a wide range of time series, which is a great advantage and of major importance to applications in business.

Exercise 1: Exponentially weighted forecasts Exercise 2: Simple exponential smoothing Exercise 3: SES vs naive Exercise 4: Exponential smoothing methods with trend Exercise 5: Holt's trend methods Exercise 6: Exponential smoothing methods with trend and seasonality Exercise 7: Holt-Winters with monthly data Exercise 8: Holt-Winters method with daily data Exercise 9: State space models for exponential smoothing Exercise 10: Automatic forecasting with exponential smoothing Exercise 11: ETS vs seasonal naive Exercise 12: Match the models to the time series Exercise 13: When does ETS fail?

ARIMA models provide another approach to time series forecasting. Exponential smoothing and ARIMA models are the two most widely-used approaches to time series forecasting, and provide complementary approaches to the problem. While exponential smoothing models are based on a description of the trend and seasonality in the data, ARIMA models aim to describe the autocorrelations in the data.

Exercise 1: Transformaties om variantie te stabiliseren Exercise 2: Box-Cox-transformaties voor tijdreeksen Exercise 3: Niet-seizoensgebonden differencing voor stationariteit Exercise 4: Seizoensdifferentiatie voor stationariteit Exercise 5: ARIMA-modellen Exercise 6: Automatische ARIMA-modellen voor niet-seizoensgebonden tijdreeksen Exercise 7: Voorspellen met ARIMA-modellen Exercise 8: auto.arima() en ets() vergelijken op niet-seizoensgebonden data Exercise 9: Seizoensgebonden ARIMA-modellen Exercise 10: Automatische ARIMA-modellen voor seizoensreeksen Exercise 11: Opties van auto.arima() verkennen

Huidige oefening

Exercise 12: auto.arima() en ets() vergelijken op seizoensdata

The time series models in the previous chapters work well for many time series, but they are often not good for weekly or hourly data, and they do not allow for the inclusion of other information such as the effects of holidays, competitor activity, changes in the law, etc. In this chapter, you will look at some methods that handle more complicated seasonality, and you consider how to extend ARIMA models in order to allow other information to be included in the them.

Exercise 1: Dynamic regression Exercise 2: Forecasting sales allowing for advertising expenditure Exercise 3: Forecasting electricity demand Exercise 4: Dynamic harmonic regression Exercise 5: Forecasting weekly data Exercise 6: Harmonic regression for multiple seasonality Exercise 7: Forecasting call bookings Exercise 8: TBATS models Exercise 9: TBATS models for electricity demand Exercise 10: Your future in forecasting!